Syrian President Bashar al-Assad is a "legitimate war criminal" and he and his circle should be treated as legitimate military targets, Sen. Lindsey Graham said Monday morning.

"I think now he is a legitimate war criminal in the eyes of the international community, and that Assad and his inner circle should be considered war criminals," the South Carolina Republican told Fox News' "Fox & Friends."

The airstrikes killed 14 people, including Iranians active in Syria. Israel's foreign ministry has not commented on the accusations.

The strikes came after President Donald Trump had promised a there was "big price to pay" for a suspected poison gas attack launched Saturday on the last remaining foothold for Syrian rebels in the eastern suburbs of Damascus. At least 40 people were killed, including women and children.

Graham, on Monday, said the United States has the ability to ground Syria's air force and air fleet, and should take action.

"We have the capability to shut them down, and we should make him pay a heavy price by destroying his air capability," Graham, a member of the Senate Armed Forces Committee, said.

In addition to destroying Syria's air capabilities, "we should set up safe zones inside of Syria, telling the Russians and the Iranians, anything left of Assad, if you cross this line we will shoot you down, so the Syrian people can regroup," he added.

The United States should also "get the Arabs involved more," said Graham, and have them "pay more, have a larger presence in Syria."

"Train up the Syrians, Arabs and Kurds to take Assad on, and get a better peace agreement at Geneva by changing the balance of power."

Meanwhile, both Iran and Russia are watching Trump, and he has the "chance to do exactly the opposite" of former President Barack Obama, the senator said, and to "send a strong signal that there is a new sheriff in town and America is back."

Trump said last week he wants to pull U.S. troops out of Syria, but Graham said Syria's regime thinks "the western world is basically already gone anyway."

"The president is yelling at the world to help him more," said Graham. "The Arabs are there but not enough of a presence. They really do believe that this will be a one and done strike, that the western world is not going to come back, that the Arabs are not going to do anything differently."

Graham said he hopes Trump will send a signal to Assad "and every other thug and dictator in the world, that 'when you cross my red lines, you may pay a heavy price.'"

"This is a very defining moment for President Trump, and I think he will rise to the occasion," he concluded.